Question

Решите срочно!! 50 БАЛЛОВ!!

Answer 1

$\left\{\begin{array}{ccc}x+y=2\\2x^{2}-xy=65 \end{array}\right \\\\\\\left\{\begin{array}{ccc}y=2-x\\2x^{2}-x\cdot(2-x)=65 \end{array}\right \\\\\\\left\{\begin{array}{ccc}y=2-x\\2x^{2}-2x+x^{2} -65=0 \end{array}\right\\\\\\\left\{\begin{array}{ccc}y=2-x\\3x^{2}-2x-65=0 \end{array}\right \\\\\\3x^{2} -2x-65=0\\\\D=(-2)^{2} -4\cdot 3\cdot (-65)=4+780=784=28^{2}\\\\x_{1} =\dfrac{2-28}{6} =-4\dfrac{1}{3}\\\\x_{2} =\dfrac{2+28}{6}=5$

$y_{1}=2-\Big(-4\dfrac{1}{3}\Big)=2+4\dfrac{1}{3}=6\dfrac{1}{3}\\\\y_{2} =2-5=-3\\\\Otvet:\boxed{\Big(-4\dfrac{1}{3} \ ; \ 6\dfrac{1}{3} \Big) \ , \ (5 \ ; \ -3)}$